New Real Madrid signing Gareth Bale, left, came on as a 58th-minute substitute for Wales in the World Cup qualifier against Serbia. Photograph: Nick Potts/PA

Gareth Bale is many things, not least the world's most expensive footballer, but even the Wales supporters who afforded him such a rapturous ovation when he came off the substitutes' bench with just over half an hour remaining must have known that it was beyond the Real Madrid forward to turn this match around.

Wales were already three goals down and in damage-limitation mode by the time Bale made his first appearance since completing his £85m move to Real Madrid. He came through his 32 minutes on the pitch unscathed but the same cannot be said for Chris Coleman, who was barracked by a section of the home fans after a sixth defeat in eight World Cup qualifiers, combined with Scotland's win in Macedonia, condemned Wales to bottom of the group.

Coleman has already agreed a new contract with the Football Association of Wales that runs until the end of the 2016 European Championship qualifying campaign and expects to sign that deal in the coming days, despite the backlash from the fans here who called for him to go.

"The contract has been agreed with the Welsh FA, I've not signed it. If I thought I couldn't affect the group of players we've got, I wouldn't waste my country's time," Coleman said. "They [the FAW] have got to be looking at the bigger picture. I'm the same man now as last week when everything was agreed."

Coleman, however, made no attempt to paper over the cracks of a performance he described as "soul-destroying". Filip Djordevic, the excellent Aleksandar Kolarov and Lazar Markovic scored the goals that underlined the gulf in class between the two sides. "There's sections of the crowd that weren't very happy and I don't blame them for reacting like that. It's been a tough two years but up until now I believe the group has been progressed," Coleman said.

Bale's name was being chanted as early as the ninth minute – a predictable response to the sight of Djordevic capitalising on some poor Wales defending to nod Serbia in front after Boaz Myhill could only parry Markovic's header. After Branislav Ivanovic and Markovic had squandered decent chances, Kolarov doubled Serbia's lead with a 25-yard shot that arrowed into the top corner.

The third goal arrived 10 minutes into the second half, when Markovic turned the ball home after Myhill, who was just about the only Wales player to emerge with any credit, had denied Dusan Tadic. That was the cue for Coleman to summon Bale, who would have marked his time on the pitch with a wonderful goal from a free-kick but for Vladimir Stojkovic's fingertip save in the closing seconds.

For Coleman, it promises to be a long month before Macedonia's visit. "We can't finish bottom, that's what we've got to look at now," he said. "I probably can't afford to lose against Macedonia. We've got to get a bit of pride back."